-
1
-
-
77749271023
-
Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
-
R. Adamczak, A. Litvak, A. Pajor, N. Tomczak-Jaegermann, Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles, J. Amer. Math. Soc. 23 (2010), 535-561.
-
(2010)
J. Amer. Math. Soc.
, vol.23
, pp. 535-561
-
-
Adamczak, R.1
Litvak, A.2
Pajor, A.3
Tomczak-Jaegermann, N.4
-
3
-
-
85007109266
-
A sharp small deviation inequality for the largest eigenvalue of a random matrix
-
Lecture Notes in Math., 1857, Springer, Berlin
-
G. Aubrun, A sharp small deviation inequality for the largest eigenvalue of a random matrix, Séminaire de Probabilités XXXVIII, 320-337, Lecture Notes in Math., 1857, Springer, Berlin, 2005.
-
(2005)
Séminaire de Probabilités
, vol.38
, pp. 320-337
-
-
Aubrun, G.1
-
4
-
-
0031534271
-
Circular law
-
Z. D. Bai, Circular law, Ann. Probab. 25 (1997), no. 1, 494-529.
-
(1997)
Ann. Probab.
, vol.25
, Issue.1
, pp. 494-529
-
-
Bai, Z.D.1
-
5
-
-
0347989448
-
Methodologies in spectral analysis of large dimensional random matrices, a review
-
Z. D. Bai, Methodologies in spectral analysis of large dimensional random matrices, a review, Statistica Sinica 9 (1999), 611-677
-
(1999)
Statistica Sinica
, vol.9
, pp. 611-677
-
-
Bai, Z.D.1
-
6
-
-
39449098318
-
-
2nd ed., Springer Series in Statistics, Springer, New York
-
Z. D. Bai, J. Silverstein, Spectral analysis of large dimensional random matrices, 2nd ed., Springer Series in Statistics, Springer, New York, 2010.
-
(2010)
Spectral Analysis of Large Dimensional Random Matrices
-
-
Bai, Z.D.1
Silverstein, J.2
-
7
-
-
38249027279
-
A note on the largest eigenvalue of a large-dimensional sample covariance matrix
-
Z. D. Bai, J. Silverstein, Y. Q. Yin, A note on the largest eigenvalue of a large-dimensional sample covariance matrix, J. Multivariate Anal. 26 (1988), 166-168.
-
(1988)
J. Multivariate Anal.
, vol.26
, pp. 166-168
-
-
Bai, Z.D.1
Silverstein, J.2
Yin, Y.Q.3
-
8
-
-
0001758959
-
Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix
-
Z. D. Bai, Y. Q. Yin, Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix, Ann. Probab. 21 (1993), 1275-1294.
-
(1993)
Ann. Probab.
, vol.21
, pp. 1275-1294
-
-
Bai, Z.D.1
Yin, Y.Q.2
-
9
-
-
55649115527
-
A simple proof of the restricted isometry property for random matrices
-
R. Baraniuk, M. Davenport, R. DeVore, M. Wakin, A simple proof of the restricted isometry property for random matrices, Constr. Approx. 28 (2008), 253-263.
-
(2008)
Constr. Approx.
, vol.28
, pp. 253-263
-
-
Baraniuk, R.1
Davenport, M.2
DeVore, R.3
Wakin, M.4
-
10
-
-
0000567685
-
p, 1 < p < 2
-
p, 1 < p < 2, Israel J. Math. 26 (1977), 178-187.
-
(1977)
Israel J. Math.
, vol.26
, pp. 178-187
-
-
Bennett, G.1
Dor, L.E.2
Goodman, V.3
Johnson, W.B.4
Newman, C.M.5
-
11
-
-
84948631966
-
The accuracy of the Gaussian approximation to the sum of independent variables
-
A. C. Berry, The accuracy of the Gaussian approximation to the sum of independent variables, Trans. Amer. Math. Soc., 49 (1941), 122-136.
-
(1941)
Trans. Amer. Math. Soc.
, vol.49
, pp. 122-136
-
-
Berry, A.C.1
-
14
-
-
84878104490
-
Compressive sampling
-
Eur. Math. Soc., Zürich
-
E. Candés, Compressive sampling, International Congress of Mathematicians. Vol. III, 1433-1452, Eur. Math. Soc., Zürich, 2006.
-
(2006)
International Congress of Mathematicians
, vol.3
, pp. 1433-1452
-
-
Candés, E.1
-
15
-
-
42649140570
-
The restricted isometry property and its implications for compressed sensing
-
E. Candés, The restricted isometry property and its implications for compressed sensing, C. R. Math. Acad. Sci. Paris 346 (2008), 589-592.
-
(2008)
C. R. Math. Acad. Sci. Paris
, vol.346
, pp. 589-592
-
-
Candés, E.1
-
17
-
-
33947416035
-
Near-optimal signal recovery from random projections: Universal encoding strategies?
-
E. Candés, T. Tao, Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inform. Theory 52 (2006), 5406-5425.
-
(2006)
IEEE Trans. Inform. Theory
, vol.52
, pp. 5406-5425
-
-
Candés, E.1
Tao, T.2
-
19
-
-
0012070851
-
Local operator theory, random matrices and banach spaces
-
North-Holland, Amsterdam
-
K. R. Davidson, S. J. Szarek, Local operator theory, random matrices and Banach spaces. Handbook of the geometry of Banach spaces, Vol. I, 317-366, North-Holland, Amsterdam, 2001.
-
(2001)
Handbook of the Geometry of Banach Spaces
, vol.1
, pp. 317-366
-
-
Davidson, K.R.1
Szarek, S.J.2
-
20
-
-
0000324960
-
Eigenvalues and condition numbers of random matrices
-
A. Edelman, Eigenvalues and condition numbers of random matrices, SIAM J. Matrix Anal. Appl. 9 (1988), 543-560
-
(1988)
SIAM J. Matrix Anal. Appl.
, vol.9
, pp. 543-560
-
-
Edelman, A.1
-
21
-
-
0010981220
-
On a lemma of littlewood and offord
-
P. Erdös, On a lemma of Littlewood and Offord, Bull. Amer. Math. Soc. 51 (1945), 898-902
-
(1945)
Bull. Amer. Math. Soc.
, vol.51
, pp. 898-902
-
-
Erdös, P.1
-
22
-
-
0010161827
-
Extremal problems in number theory
-
AMS, Providence, R.I.
-
P. Erdös, Extremal problems in number theory, 1965 Proc. Sympos. Pure Math., Vol. VIII, pp. 181-189 AMS, Providence, R.I.
-
1965 Proc. Sympos. Pure Math.
, vol.8
, pp. 181-189
-
-
Erdös, P.1
-
23
-
-
34250598875
-
Fourier analysis of distribution functions. A mathematical study of the laplace Gaussian law
-
C. G. Esseen, Fourier analysis of distribution functions. A mathematical study of the laplace Gaussian law, Acta Math. 77 (1945), 1-125.
-
(1945)
Acta Math.
, vol.77
, pp. 1-125
-
-
Esseen, C.G.1
-
24
-
-
0012869144
-
On the kolmogorov-rogozin inequality for the concentration function
-
C. G. Esseen, On the Kolmogorov-Rogozin inequality for the concentration function, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 5 (1966), 210-216.
-
(1966)
Z. Wahrscheinlichkeitstheorie und Verw. Gebiete
, vol.5
, pp. 210-216
-
-
Esseen, C.G.1
-
25
-
-
84877877878
-
A universality result for the smallest eigenvalues of certain sample covariance matrices
-
to appear
-
O. Feldheim, S. Sodin, A universality result for the smallest eigenvalues of certain sample covariance matrices, Geometric and Functional Analysis, to appear
-
Geometric and Functional Analysis
-
-
Feldheim, O.1
Sodin, S.2
-
26
-
-
0037663571
-
Solution of the littlewood-offord problem in high dimensions
-
P. Frankl, Z. Füredi, Solution of the Littlewood-Offord problem in high dimensions, Ann. of Math. (2) 128 (1988), 259-270.
-
(1988)
Ann. of Math. (2)
, vol.128
, pp. 259-270
-
-
Frankl, P.1
Füredi, Z.2
-
27
-
-
36049009154
-
Bounds on the concentration function in terms of the diophantine approximation
-
O. Friedland, S. Sodin, Bounds on the concentration function in terms of the Diophantine approximation, C. R. Math. Acad. Sci. Paris 345 (2007), 513-518.
-
(2007)
C. R. Math. Acad. Sci. Paris
, vol.345
, pp. 513-518
-
-
Friedland, O.1
Sodin, S.2
-
28
-
-
3543141538
-
The widths of a euclidean ball
-
A. Garnaev, E. Gluskin, The widths of a Euclidean ball, Soviet Math. Dokl. 30 (1984), 200-204.
-
(1984)
Soviet Math. Dokl.
, vol.30
, pp. 200-204
-
-
Garnaev, A.1
Gluskin, E.2
-
29
-
-
0001436319
-
A limit theorem for the norm of random matrices
-
S. Geman, A limit theorem for the norm of random matrices, Ann. Probab. 8 (1980), 252-261.
-
(1980)
Ann. Probab.
, vol.8
, pp. 252-261
-
-
Geman, S.1
-
30
-
-
0001393752
-
The circular law
-
V. L. Girko, The circular law, Theory Probab. Appl. 29 (1984), no. 4, 694-706.
-
(1984)
Theory Probab. Appl.
, vol.29
, Issue.4
, pp. 694-706
-
-
Girko, V.L.1
-
32
-
-
51249179500
-
Some inequalities for Gaussian processes and applications
-
Y. Gordon, Some inequalities for Gaussian processes and applications, Israel J. Math. 50 (1985), 265-289.
-
(1985)
Israel J. Math.
, vol.50
, pp. 265-289
-
-
Gordon, Y.1
-
33
-
-
0011597392
-
Majorization of Gaussian processes and geometric applications
-
Y. Gordon, Majorization of Gaussian processes and geometric applications, Probab. Theory Related Fields 91 (1992), 251-267.
-
(1992)
Probab. Theory Related Fields
, vol.91
, pp. 251-267
-
-
Gordon, Y.1
-
37
-
-
0034340689
-
Shape fluctuations and random matrices
-
K. Johansson, Shape fluctuations and random matrices, Comm. Math. Phys. 209 (2000), 437-476.
-
(2000)
Comm. Math. Phys.
, vol.209
, pp. 437-476
-
-
Johansson, K.1
-
39
-
-
0035641726
-
On the distribution of the largest eigenvalue in principal components analysis
-
I. M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist. 29 (2001), 295-327.
-
(2001)
Ann. Statist.
, vol.29
, pp. 295-327
-
-
Johnstone, I.M.1
-
40
-
-
33645673056
-
Estimates for the concentration function of combinatorial number theory and probability
-
G. Halász, Estimates for the concentration function of combinatorial number theory and probability, Periodica Mathematica Hungarica 8 (1977), 197-211
-
(1977)
Periodica Mathematica Hungarica
, vol.8
, pp. 197-211
-
-
Halász, G.1
-
41
-
-
0001387808
-
Section of some finite-dimensional sets and classes of smooth functions
-
(in Russian)
-
B. Kashin, Section of some finite-dimensional sets and classes of smooth functions (in Russian) Izv. Acad. Nauk. SSSR 41 (1977) 334-351.
-
(1977)
Izv. Acad. Nauk. SSSR
, vol.41
, pp. 334-351
-
-
Kashin, B.1
-
42
-
-
1842484669
-
Sur les propriétés des fonctions de concentrations de M. P. Lévy
-
A. Kolmogorov, Sur les propriétés des fonctions de concentrations de M. P. Lévy, Ann. Inst. H. Poincaré 16 (1958), 27-34.
-
(1958)
Ann. Inst. H. Poincaré
, vol.16
, pp. 27-34
-
-
Kolmogorov, A.1
-
43
-
-
84968494236
-
On the probability that a random ±1-matrix is singular
-
J. Kahn, J. Komlós, E. Szemerédi, On the probability that a random ±1-matrix is singular, J. Amer. Math. Soc. 8 (1995), 223-240.
-
(1995)
J. Amer. Math. Soc.
, vol.8
, pp. 223-240
-
-
Kahn, J.1
Komlós, J.2
Szemerédi, E.3
-
44
-
-
0004108913
-
On the determinant of (0, 1) matrices
-
J. Komlós, On the determinant of (0, 1) matrices, Studia Sci. Math. Hungar. 2 (1967), 7-22.
-
(1967)
Studia Sci. Math. Hungar.
, vol.2
, pp. 7-22
-
-
Komlós, J.1
-
45
-
-
25544469014
-
On the determinant of random matrices
-
J. Komlós, On the determinant of random matrices, Studia Sci. Math. Hungar. 3 (1968), 387-399.
-
(1968)
Studia Sci. Math. Hungar.
, vol.3
, pp. 387-399
-
-
Komlós, J.1
-
46
-
-
18144366601
-
Some estimates of norms of random matrices
-
R. Latala, Some estimates of norms of random matrices, Proc. Amer. Math. Soc. 133 (2005), 1273-1282.
-
(2005)
Proc. Amer. Math. Soc.
, vol.133
, pp. 1273-1282
-
-
Latala, R.1
-
47
-
-
0012942540
-
The concentration of measure phenomenon. Mathematical surveys and monographs
-
Providence, RI
-
M. Ledoux, The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, RI, 2001.
-
(2001)
American Mathematical Society
, vol.89
-
-
Ledoux, M.1
-
48
-
-
34247605051
-
Deviation inequalities on largest eigenvalues
-
Lecture Notes in Math. Springer, Berlin
-
M. Ledoux, Deviation inequalities on largest eigenvalues, Geometric aspects of functional analysis, 167-219, Lecture Notes in Math., 1910, Springer, Berlin, 2007.
-
(1910)
Geometric Aspects of Functional Analysis
, pp. 167-219
-
-
Ledoux, M.1
-
49
-
-
0003372425
-
Probability in banach spaces. Isoperimetry and processes
-
Springer Verlag, Berlin
-
M. Ledoux, M. Talagrand, Probability in Banach spaces. Isoperimetry and processes. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 23. Springer Verlag, Berlin, 1991.
-
(1991)
Ergebnisse der Mathematik und Ihrer Grenzgebiete
, vol.23
, Issue.3
-
-
Ledoux, M.1
Talagrand, M.2
-
51
-
-
70350344396
-
Gaussian processes: Inequalities, small ball probabilities and applications
-
Handbook of Statistics, 19, North-Holland, Amsterdam
-
W. V. Li, Q.-M. Shao, Gaussian processes: inequalities, small ball probabilities and applications. Stochastic processes: theory and methods, 533-597, Handbook of Statistics, 19, North-Holland, Amsterdam, 2001.
-
(2001)
Stochastic Processes: Theory and Methods
, pp. 533-597
-
-
Li, W.V.1
Shao, Q.-M.2
-
52
-
-
0005272276
-
On the number of real roots of a random algebraic equation
-
III
-
J. E. Littlewood, A. C. Offord, On the number of real roots of a random algebraic equation. III. Rec. Math. [Mat. Sbornik] N.S. 12(54), (1943), 277-286
-
(1943)
Rec. Math. [Mat. Sbornik] N.S.
, vol.12
, Issue.54
, pp. 277-286
-
-
Littlewood, J.E.1
Offord, A.C.2
-
53
-
-
18644382839
-
Smallest singular value of random matrices and geometry of random polytopes
-
A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005), 491-523.
-
(2005)
Adv. Math.
, vol.195
, pp. 491-523
-
-
Litvak, A.1
Pajor, A.2
Rudelson, M.3
Tomczak-Jaegermann, N.4
-
54
-
-
29244449653
-
Euclidean embeddings in spaces of finite volume ratio via random matrices
-
A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin, Euclidean embeddings in spaces of finite volume ratio via random matrices, J. Reine Angew. Math. 589 (2005), 1-19.
-
(2005)
J. Reine Angew. Math.
, vol.589
, pp. 1-19
-
-
Litvak, A.E.1
Pajor, A.2
Rudelson, M.3
Tomczak-Jaegermann, N.4
Vershynin, R.5
-
55
-
-
0000263239
-
The distribution of eigenvalues in certain sets of random matrices
-
V. A. Marchenko, L. A. Pastur, The distribution of eigenvalues in certain sets of random matrices, Mat. Sb., 72 (1967), 507-536.
-
(1967)
Mat. Sb.
, vol.72
, pp. 507-536
-
-
Marchenko, V.A.1
Pastur, L.A.2
-
57
-
-
55649100730
-
Uniform uncertainty principle for bernoulli and Subgaussian ensembles
-
S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Uniform uncertainty principle for Bernoulli and subgaussian ensembles, Constr. Approx. 28 (2008), 277-289.
-
(2008)
Constr. Approx.
, vol.28
, pp. 277-289
-
-
Mendelson, S.1
Pajor, A.2
Tomczak-Jaegermann, N.3
-
58
-
-
0002417176
-
A new proof of the theorem of A. Dvoretzky on sections of convex bodies
-
V. Milman, A new proof of the theorem of A. Dvoretzky on sections of convex bodies, Funct. Anal. Appl. 5 (1971), 28-37.
-
(1971)
Funct. Anal. Appl.
, vol.5
, pp. 28-37
-
-
Milman, V.1
-
60
-
-
0002728031
-
On the spectrum of random matrices
-
L. A Pastur, On the spectrum of random matrices, Teoret. Mat. Fiz. 10 (1973), 102-112.
-
(1973)
Teoret. Mat. Fiz.
, vol.10
, pp. 102-112
-
-
Pastur, L.A.1
-
61
-
-
0008529642
-
Sums of independent random variables
-
Springer-Verlag, New York-Heidelberg
-
V. V. Petrov, Sums of independent random variables. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 82. Springer-Verlag, New York-Heidelberg, 1975.
-
(1975)
Ergebnisse der Mathematik und Ihrer Grenzgebiete
, vol.82
-
-
Petrov, V.V.1
-
62
-
-
31344479578
-
Lower estimates for the singular values of random matrices
-
M. Rudelson, Lower estimates for the singular values of random matrices, C. R. Math. Acad. Sci. Paris 342 (2006), 247-252.
-
(2006)
C. R. Math. Acad. Sci. Paris
, vol.342
, pp. 247-252
-
-
Rudelson, M.1
-
63
-
-
49649108303
-
Invertibility of random matrices: Norm of the inverse
-
M. Rudelson, Invertibility of random matrices: norm of the inverse, Annals of Mathematics 168 (2008), 575-600.
-
(2008)
Annals of Mathematics
, vol.168
, pp. 575-600
-
-
Rudelson, M.1
-
65
-
-
41049114969
-
The littlewood-offord problem and invertibility of random matrices
-
M. Rudelson, R. Vershynin, The Littlewood-Offord problem and invertibility of random matrices, Adv. Math. 218 (2008), 600-633.
-
(2008)
Adv. Math.
, vol.218
, pp. 600-633
-
-
Rudelson, M.1
Vershynin, R.2
-
67
-
-
76749128899
-
Smallest singular value of a random rectangular matrix
-
M. Rudelson, R. Vershynin, Smallest singular value of a random rectangular matrix, Comm. Pure Appl. Math. 62 (2009), 1707-1739.
-
(2009)
Comm. Pure Appl. Math.
, vol.62
, pp. 1707-1739
-
-
Rudelson, M.1
Vershynin, R.2
-
68
-
-
34247360062
-
Smoothed analysis of the condition numbers and growth factors of matrices
-
A. Sankar, D. A. Spielman, S.-H. Teng, Smoothed analysis of the condition numbers and growth factors of matrices, SIAM J. Matrix Anal. Appl. 28 (2006), 446-476.
-
(2006)
SIAM J. Matrix Anal. Appl.
, vol.28
, pp. 446-476
-
-
Sankar, A.1
Spielman, D.A.2
Teng, S.-H.3
-
69
-
-
26744445544
-
Über ein Problem von Erdös und Moser
-
A. Sárközy, E. Szeméredi, Über ein Problem von Erdös und Moser, Acta Arithmetica 11 (1965), 205-208
-
(1965)
Acta Arithmetica
, vol.11
, pp. 205-208
-
-
Sárközy, A.1
Szeméredi, E.2
-
70
-
-
51249186089
-
Random embeddings of euclidean spaces in sequence spaces
-
G. Schechtman, Random embeddings of Euclidean spaces in sequence spaces, Israel Journal of Mathematics 40, No. 2, 1981, 187-192.
-
(1981)
Israel Journal of Mathematics
, vol.40
, Issue.2
, pp. 187-192
-
-
Schechtman, G.1
-
71
-
-
0001629248
-
The smallest eigenvalue of a large-dimensional wishart matrix
-
J. Silverstein, The smallest eigenvalue of a large-dimensional Wishart matrix, Ann. Probab. 13 (1985), 1364-1368.
-
(1985)
Ann. Probab.
, vol.13
, pp. 1364-1368
-
-
Silverstein, J.1
-
72
-
-
84944485006
-
The one-sided barrier problem for Gaussian noise
-
D. Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463-501.
-
(1962)
Bell System Tech. J.
, vol.41
, pp. 463-501
-
-
Slepian, D.1
-
73
-
-
84967770163
-
On the efficiency of algorithms of analysis
-
S. Smale, On the efficiency of algorithms of analysis, Bull. Amer. Math. Soc. (N.S.) 13 (1985), 87-121
-
(1985)
Bull. Amer. Math. Soc. (N.S.)
, vol.13
, pp. 87-121
-
-
Smale, S.1
-
74
-
-
0141450345
-
A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
-
A. Soshnikov, A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices, J. Statist. Phys. 108 (2002), 1033-1056.
-
(2002)
J. Statist. Phys.
, vol.108
, pp. 1033-1056
-
-
Soshnikov, A.1
-
75
-
-
35248849703
-
Smoothed analysis of algorithms
-
Beijing Higher Ed. Press, Beijing, 2002
-
D. Spielman, S.-H. Teng, Smoothed analysis of algorithms. Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), 597-606, Higher Ed. Press, Beijing, 2002
-
(2002)
Proceedings of the International Congress of Mathematicians
, vol.1
, pp. 597-606
-
-
Spielman, D.1
Teng, S.-H.2
-
76
-
-
51249165477
-
Concentration of measure and isoperimetric inequalities in product spaces
-
M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Inst. Hautes Études Sci. Publ. Math. No. 81 (1995), 73-205.
-
(1995)
Inst. Hautes Études Sci. Publ. Math. No. 81
, pp. 73-205
-
-
Talagrand, M.1
-
77
-
-
0030522124
-
A new look at independence
-
M. Talagrand, A new look at independence, Ann. Probab. 24 (1996), 1-34.
-
(1996)
Ann. Probab.
, vol.24
, pp. 1-34
-
-
Talagrand, M.1
-
78
-
-
33645288547
-
On random ±1 matrices: Singularity and determinant
-
T. Tao, V. Vu, On random ±1 matrices: singularity and determinant, Random Structures and Algorithms 28 (2006), 1-23.
-
(2006)
Random Structures and Algorithms
, vol.28
, pp. 1-23
-
-
Tao, T.1
Vu, V.2
-
79
-
-
0009400517
-
Condition numbers of random matrices
-
S. Szarek, Condition numbers of random matrices, J. Complexity 7 (1991), 131-149.
-
(1991)
J. Complexity
, vol.7
, pp. 131-149
-
-
Szarek, S.1
-
80
-
-
33947248273
-
Additive combinatorics
-
Cambridge University Press, Cambridge
-
T. Tao, V. Vu, Additive combinatorics. Cambridge Studies in Advanced Mathematics, 105. Cambridge University Press, Cambridge, 2006.
-
(2006)
Cambridge Studies in Advanced Mathematics
, vol.105
-
-
Tao, T.1
Vu, V.2
-
81
-
-
41049103477
-
On the singularity probability of random bernoulli matrices
-
T. Tao, V. Vu, On the singularity probability of random Bernoulli matrices, J. Amer. Math. Soc. 20 (2007), 603-628.
-
(2007)
J. Amer. Math. Soc.
, vol.20
, pp. 603-628
-
-
Tao, T.1
Vu, V.2
-
82
-
-
44249125025
-
Random matrices: The circular law
-
T. Tao, V. Vu, Random matrices: the circular law, Commun. Contemp. Math. 10 (2008), no. 2, 261-307.
-
(2008)
Commun. Contemp. Math.
, vol.10
, Issue.2
, pp. 261-307
-
-
Tao, T.1
Vu, V.2
-
83
-
-
71849089047
-
Inverse littlewood-offord theorems and the condition number of random discrete matrices
-
T. Tao, V. Vu, Inverse Littlewood-Offord theorems and the condition number of random discrete matrices, Annals of Math. 169 (2009), 595-632.
-
(2009)
Annals of Math.
, vol.169
, pp. 595-632
-
-
Tao, T.1
Vu, V.2
-
84
-
-
68949196333
-
From the littlewood-offord problem to the circular law: Universality of the spectral distribution of random matrices
-
T. Tao, V. Vu, From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices, Bull. Amer. Math. Soc. 46 (2009), 377-396.
-
(2009)
Bull. Amer. Math. Soc.
, vol.46
, pp. 377-396
-
-
Tao, T.1
Vu, V.2
-
87
-
-
84877883004
-
Random matrices: The distribution of smallest singular values
-
to appear
-
T. Tao, V. Vu, Random matrices: the distribution of smallest singular values, Geom. Funct. Anal., to appear
-
Geom. Funct. Anal.
-
-
Tao, T.1
Vu, V.2
-
89
-
-
27644532196
-
Level-spacing distributions and the airy kernel
-
C. Tracy, H. Widom, Level-Spacing Distributions and the Airy Kernel, Comm. Math. Phys. 159 (1994), 151-174.
-
(1994)
Comm. Math. Phys.
, vol.159
, pp. 151-174
-
-
Tracy, C.1
Widom, H.2
-
90
-
-
0030545965
-
On orthogonal and symplectic matrix ensembles
-
C. Tracy, H. Widom, On orthogonal and symplectic matrix ensembles, Comm. Math. Phys. 177 (1996), no. 3, 727-754.
-
(1996)
Comm. Math. Phys.
, vol.177
, Issue.3
, pp. 727-754
-
-
Tracy, C.1
Widom, H.2
-
91
-
-
3042622312
-
Distribution functions for largest eigenvalues and their applications
-
Beijing Higher Ed. Press, Beijing, 2002
-
C. Tracy, H. Widom, Distribution functions for largest eigenvalues and their applications, Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), 587-596, Higher Ed. Press, Beijing, 2002.
-
(2002)
Proceedings of the International Congress of Mathematicians
, vol.1
, pp. 587-596
-
-
Tracy, C.1
Widom, H.2
-
92
-
-
0001252659
-
Numerical inverting of matrices of high order
-
J. von Neumann, H. H. Goldstine, Numerical inverting of matrices of high order, Bull. Amer. Math. Soc. 53 (1947), 1021-1099.
-
(1947)
Bull. Amer. Math. Soc.
, vol.53
, pp. 1021-1099
-
-
Von Neumann, J.1
Goldstine, H.H.2
-
93
-
-
85027937377
-
Spectral norm of products of random and deterministic matrices
-
DOI: 10.1007/s00440-010-0281-z
-
R. Vershynin, Spectral norm of products of random and deterministic matrices, Probability Theory and Related Fields, DOI: 10.1007/s00440-010-0281-z.
-
Probability Theory and Related Fields
-
-
Vershynin, R.1
-
95
-
-
0002247902
-
Strong limits of random matrix spectra for sample covariance matrices of independent elements
-
K. W. Wachter, Strong limits of random matrix spectra for sample covariance matrices of independent elements, Annals of Probability 6 (1978), 1-18.
-
(1978)
Annals of Probability
, vol.6
, pp. 1-18
-
-
Wachter, K.W.1
-
96
-
-
0001560594
-
On the distribution of the roots of certain symmetric matrices
-
P. Wigner, On the distribution of the roots of certain symmetric matrices, Annals of Mathematics 67 (1958), 325-327.
-
(1958)
Annals of Mathematics
, vol.67
, pp. 325-327
-
-
Wigner, P.1
-
97
-
-
0001136512
-
On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix
-
Y. Q. Yin, Z. D. Bai, P. R. Krishnaiah, On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix, Probab. Theory Related Fields 78 (1988), 509-521.
-
(1988)
Probab. Theory Related Fields
, vol.78
, pp. 509-521
-
-
Yin, Y.Q.1
Bai, Z.D.2
Krishnaiah, P.R.3
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